Answer:
square root -91/3
Step-by-step explanation:
just took the test
The right option is missing. The correct answer is tan(0) = -(√91)/3.
The trigonometric expression tan(0) has a value of -(√91)/3 when cos(0) = -3/10.
The values of all trigonometric functions dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides about any of its acute angles are known as that angle's trigonometric ratios.
The three sides of the right-angled triangle are:
Hypotenuse (the longest side)
Perpendicular (opposite side to the angle)
Base (Adjacent side to the angle)
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
The trigonometry ratios for a specific angle ‘θ’ is given below:
Trigonometric Ratios:
Sin θ = Perpendicular/Hypotenuse
Cos θ = Base/Hypotenuse
Tan θ = Perpendicular/Base or Sin θ/Cos θ
Cot θ = Base/Perpendicular or 1/tan θ
Sec θ = Hypotenuse/Base or 1/cos θ
Cosec θ = Hypotenuse/Perpendicular or 1/sin θ
According to the Pythagoras theorem, we can say that in a right-angled triangle:
Hypotenuese² = Base² + Perpendicular²
We are given cos(0) = -3/10, 0 being an obtuse angle (90° < 0 < 180°, since 0 is an angle in quadrant II)
We need to remember that in quadrant II, sine is always positive, cosine is negative, and tangent is also negative.
We are asked to find the value of tan(0).
We know cos(0) = Base/Hypotenuse.
So we let the hypotenuse be 10k, and let the base be 3k. Let the perpendicular be p.
By Pythagoras' Theorem,
Hypotenuese² = Base² + Perpendicular²
or, (10k)² = (3k)² + p²
or, 100k² = p² + 9k²
or, p² = 100k² - 9k² = 91k² = (k√91)²
or, p = k√91
Now, we can find the value of tan(0):
tan(0) = Perpendicular/Base = -(k√91)/3k = -(√91)/3
(Negative value taken as tan is negative in quadrant II)
∴ The trigonometric expression tan(0) has a value of -(√91)/3 when cos(0) = -3/10.
Learn more about trigonometric expressions at
brainly.com/question/7331447
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